dc.contributor.advisor Çetin, A. Enis dc.contributor.author Tofighi, Mohammad dc.date.accessioned 2016-07-01T11:11:03Z dc.date.available 2016-07-01T11:11:03Z dc.date.issued 2015 dc.identifier.uri http://hdl.handle.net/11693/30038 dc.description Cataloged from PDF version of article. en_US dc.description.abstract This thesis focuses on image restoration and reconstruction problems. These en_US inverse problems are solved using a convex optimization algorithm based on orthogonal Projections onto the Epigraph Set of a Convex Cost functions (PESC). In order to solve the convex minimization problem, the dimension of the problem is lifted by one and then using the epigraph concept the feasibility sets corresponding to the cost function are defined. Since the cost function is a convex function in R N , the corresponding epigraph set is also a convex set in R N+1. The convex optimization algorithm starts with an arbitrary initial estimate in R N+1 and at each step of the iterative algorithm, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The PESC algorithm provides globally optimal solutions for different functions such as total variation, 1-norm, 2-norm, and entropic cost functions. Denoising, deconvolution and compressive sensing are among the applications of PESC algorithm. The Projection onto Epigraph Set of Total Variation function (PES-TV) is used in 2-D applications and for 1-D applications Projection onto Epigraph Set of 1-norm cost function (PES-1) is utilized. In PES-1 algorithm, first the observation signal is decomposed using wavelet or pyramidal decomposition. Both wavelet denoising and denoising methods using the concept of sparsity are based on soft-thresholding. In sparsity-based denoising methods, it is assumed that the original signal is sparse in some transform domain such as Fourier, DCT, and/or wavelet domain and transform domain coefficients of the noisy signal are soft-thresholded to reduce noise. Here, the relationship between the standard soft-thresholding based denoising methods and sparsity-based wavelet denoising methods is described. A deterministic soft-threshold estimation method using the epigraph set of 1-norm cost function is presented. It is demonstrated that the size of the 1-ball can be determined using linear algebra. The size of the 1-ball in turn determines the soft-threshold. The PESC, PES-TV and PES-1 algorithms, are described in detail in this thesis. Extensive simulation results are presented. PESC based inverse restoration and reconstruction algorithm is compared to the state of the art methods in the literature. dc.description.statementofresponsibility Tofighi, Mohammad en_US dc.format.extent xxi, 102 leaves, Charts en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Convex optimization en_US dc.subject epigraph of a convex cost functions en_US dc.subject projection en_US onto convex sets dc.subject total variation function en_US dc.subject 1-norm function en_US dc.subject denoising en_US dc.subject deconvolution en_US dc.subject compressive sensing en_US dc.subject.lcc B150951 en_US dc.title Image restoration and reconstruction using projections onto epigraph set of convex cost fuchtions en_US dc.type Thesis en_US dc.department Department of Electrical and Electronics Engineering en_US dc.publisher Bilkent University en_US dc.description.degree M.S. en_US dc.identifier.itemid B150951
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